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Theorem simp1r2 1369
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1r2 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜓)

Proof of Theorem simp1r2
StepHypRef Expression
1 simpr2 1250 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant1 1163 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385  df-3an 1109
This theorem is referenced by:  monmatcollpw  20863  lshpkrlem6  35071  atbtwnexOLDN  35403  atbtwnex  35404  3dim3  35425  4atlem11  35565  4atexlem7  36031  cdleme22b  36297
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